Draw five parallel lines in the horizontal direction first, and then draw two parallel lines in the vertical direction. These seven straight lines * * * have 2*5= 10 intersections.

Then draw three parallel lines in directions that are not parallel to the horizontal and vertical directions. These three parallel lines have 3*7=2 1 intersection points with the above seven straight lines. Ensure that intersections do not overlap.

So ten straight lines have thirty-one intersections.

It can be understood that

3 1=9+8+7+6+ 1

The first six straight lines intersect at 1, and the other four straight lines intersect with the previous one.